Multiply the following complex numbers: $({4+2i}) \cdot ({2})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4+2i}) \cdot ({2}) = $ $ ({4} \cdot {2}) + ({4} \cdot {0}i) + ({2}i \cdot {2}) + ({2}i \cdot {0}i) $ Then simplify the terms: $ (8) + (0i) + (4i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 8 + (0 + 4)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 8 + (0 + 4)i - 0 $ The result is simplified: $ (8 - 0) + (4i) = 8+4i $